Question

A ball $A$ is falling vertically downwards with velocity $v_1$. It strikes elastically with a wedge moving horizontally with velocity $v_2$ as shown in figure. What must be the ratio so that the ball bounces back in vertically upwards direction relative to wedge?

• A. $\sqrt{3}$
• B. $\frac{1}{\sqrt{3}}$
• C. 2
• D. $\frac{1}{2}$

Answer 1

The correct option is B

$\frac{1}{\sqrt{3}}$

In the figure $v_{12}$ = velocity of ball w.r.t wedge before collision and $v_{12}$ = velocity of ball w.r.t wedge after collision, which must be in vertically upward direction as shown. In elastic collision $v_{12}$ and $v_{12}$ will make equal angle (say) with the normal to the plane.

We can show that $\alpha$ = ${30}^{\circ }$

$\therefore \angle MON$ = ${30}^{\circ }$

Now $\frac{v_1}{v_2}$ = $tan{30}^{\circ }$ = $\frac{1}{\sqrt{3}}$